Point-Slope Form

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you identify the slope from a point-slope equation?

Back

The slope (m) is the coefficient of (x - x1) in the point-slope form equation.

Front

Convert the point-slope equation y - 2 = 4(x + 1) to slope-intercept form.

Back

y = 4x + 6.

Front

What does the term 'slope' represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

If a line has a slope of -2, what does this indicate about its direction?

Back

A slope of -2 indicates that the line descends from left to right.

Front

What is the significance of the point (x1, y1) in the point-slope form?

Back

The point (x1, y1) is a specific point on the line that the equation represents.

Front

How can you determine if a point lies on the line represented by a point-slope equation?

Back

Substitute the x and y coordinates of the point into the equation. If the equation holds true, the point lies on the line.

Front

What is the slope of the line represented by the equation y + 3 = 2(x - 1)?

Back

The slope is 2.

Front

Which of the following is a correct point-slope equation for the line with slope 3 passing through the point (2, 5)?

Back

y - 5 = 3(x - 2).

Front

Convert the equation y - 1 = -1/2(x + 4) into slope-intercept form.

Back

y = -1/2x - 1.